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Combine the mince with the onion and half the parsley, then season. Shape into four burger patties about 8cm wide and 1cm deep. Heat a griddle pan over a high heat and brush each burger with the oil on both sides. When the pan is really hot, add the burgers and cook for 5 mins each side until charred and cooked through.
Meanwhile, prepare the slaw by combining the fennel, spring onions and carrot in a large bowl. Add the mayo and remaining parsley, then squeeze over the juice of two lemon wedges. Season well and set aside.
Halve the buns and griddle for 1-2 mins until griddle lines appear. Put the burger in the bun, top with the fennel slaw and serve with a lemon wedge for squeezing over.